Regression & factor
analyses …
Regression example - revisited
 Our example:
 A financial company wishes to ascertain what the drivers of
satisfaction are for their service: They are:
EXPERT="experts"
Q30A2 ="Take the time to understand who you are"
Q30A3 ="Communicate clearly, in plain language"
Q30A6 ="Go out of their way to tailor the best deal"
Q30A7 ="Have the knowledge and authority to make"
Q30A8 ="Have a positive, can-do approach"
Q30A11 ="Understand your business and the market"
Q30A12 ="Are proactive with ideas on how to get t"
Q30A13 ="Are prompt and reliable in handling any"
Q30A14 ="Treat you with respect and listen"
Q30A15 ="Keep in regular contact to keep you updated"
Q32A1
="The competitiveness of their fees and rates"
Q32A2
="Offering a flexible range of lending/rep"
Q32A3
="How easy it is to take out a commercial"
Q32A4
="The features and benefits of their comments"
Q32A5
="Providing a full range of commercial product"
Q32A6
="Being fair and reasonable in their lending“
Q24 ="Q3a. AMP BANKING OVERALL RATING“
NB: this is the response
 These were all on a 10 point scale
Let’s do a factor analysis
proc factor data = hold.model rotate =varimax fuzz=.3 nfact=3;
var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11 Q30A12 Q30A13
Q30A14 Q30A15
Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6;
run;
Rotated Factor Pattern
EXPERT
Q30A2
Q30A3
Q30A6
Q30A7
Q30A8
Q30A11
Q30A12
Q30A13
Q30A14
Q30A15
Q32A1
Q32A2
Q32A3
Q32A4
Q32A5
Q32A6
STAFF - Experts in Commercial Finance Ma
Take the time to understand who you are
Communicate clearly, in plain language
Go out of their way to tailor the best d
Have the knowledge and authority to make
Have a positive, can-do approach to doin
Understand your business and the market
Are proactive with ideas on how to get t
Are prompt and reliable in handling any
Treat you with respect and listen to wha
Keep in regular contact to keep you upda
The competitiveness of their fees and ra
Offering a flexible range of lending/rep
How easy it is to take out a commercial
The features and benefits of their comme
Providing a full range of commercial and
Being fair and reasonable in their lendi
Values less than 0.5 are not printed.
Factor1
Factor2
Factor3
.
.
0.58922
.
0.67551
0.70404
0.51376
.
0.78677
0.77983
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0.76013
0.74967
0.67490
0.76336
0.61487
0.74213
0.51465
0.72096
0.51987
.
.
.
0.66569
0.68897
.
.
0.79008
.
.
.
.
.
.
Let’s do a factor analysis
proc factor data = hold.model rotate =varimax fuzz=.5 nfact=4;
var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11 Q30A12 Q30A13
Q30A14 Q30A15
Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6;
run;
Rotated Factor Pattern
EXPERT
Q30A2
Q30A3
Q30A6
Q30A7
Q30A8
Q30A11
Q30A12
Q30A13
Q30A14
Q30A15
Q32A1
Q32A2
Q32A3
Q32A4
Q32A5
Q32A6
STAFF - Experts in Commercial Finance Ma
Take the time to understand who you are
Communicate clearly, in plain language
Go out of their way to tailor the best d
Have the knowledge and authority to make
Have a positive, can-do approach to doin
Understand your business and the market
Are proactive with ideas on how to get t
Are prompt and reliable in handling any
Treat you with respect and listen to wha
Keep in regular contact to keep you upda
The competitiveness of their fees and ra
Offering a flexible range of lending/rep
How easy it is to take out a commercial
The features and benefits of their comme
Providing a full range of commercial and
Being fair and reasonable in their lendi
Values less than 0.5 are not printed.
Factor1
Factor2
Factor3
Factor4
0.57635
0.70602
0.51025
0.53333
.
0.51991
0.67486
0.73501
.
.
0.78844
.
.
.
.
.
.
.
.
0.59210
.
.
0.59144
.
.
0.75572
0.84713
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0.80252
0.50843
.
0.78841
0.59441
0.67644
.
.
.
.
0.59786
.
.
.
.
.
.
.
0.66142
0.72790
.
.
.
Let’s go for three factors
 Communication:
 Products:
 Expertise:
How do we go about regressing
these?
 First save the factor output to a file and rename :
proc factor data = hold.model out =hold.model* outstat =hold.modelfac**
rotate =varimax fuzz=.5 nfact=3;
var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11 Q30A12 Q30A13
Q30A14
Q30A15
Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6;
run;
data hold.model;
set hold.model;
rename
factor1 = comms
factor2 = prod
factor3 = expt;
run;
* This just put output for Factor1-3 on the end of the file hold.model;
** this yields all the stats used in the FA
Regressing the factors
proc reg data =hold.model;
model Q24 = comms prod expt;
run;
proc reg data =hold.model;
model Q24 = comms prod expt;
run;
Dependent Variable: Q24 Q3a. AMP BANKING OVERALL RATING
Analysis of Variance
DF
Sum of
Squares
Mean
Square
3
296
299
501.84288
583.12712
1084.97000
167.28096
1.97002
Root MSE
Dependent Mean
Coeff Var
1.40358
7.51000
18.68942
Source
Model
Error
Corrected Total
R-Square
Adj R-Sq
F Value
Pr > F
84.91
<.0001
0.4625
0.4571
Parameter Estimates
Variable
Label
Intercept
COMMS
PROD
EXPT
Intercept
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
1
1
1
1
7.51000
0.96331
0.56340
0.65804
0.08104
0.08117
0.08117
0.08117
92.68
11.87
6.94
8.11
<.0001
<.0001
<.0001
<.0001
Conclude
We conclude that:
 Note also the orthogonality (linear indepedence of the
factors)
Pearson Correlation Coefficients, N = 300
Prob > |r| under H0: Rho=0
COMMS
PROD
COMMS
PROD
EXPT
1.00000
0.00000
0.00000
1.0000
1.0000
1.00000
0.00000
0.00000
1.0000
EXPT
1.0000
0.00000
0.00000
1.0000
1.0000
1.00000
 Note also that usual regression checks should apply (not
done here - but will need to be inspected by you!)
Getting to the actual attributes
 This is all very well to recommend more emphasis on
communication - but just which components do we need to
look at?
 Easy look at the combination of regression coefficients with
the scoring parameters for each driver:
COMMS
PROD
EXPT
and
1
1
1
0.96331
0.56340
0.65804
0.08117
0.08117
0.08117
11.87
6.94
8.11
<.0001
<.0001
<.0001
Standardized Scoring Coefficients
EXPERT
Q30A2
Q30A3
Q30A6
Q30A7
Q30A8
Q30A11
Q30A12
Q30A13
Q30A14
Q30A15
Q32A1
Q32A2
Q32A3
Q32A4
Q32A5
Q32A6
STAFF - Experts in Commercial Finance Ma
Take the time to understand who you are
Communicate clearly, in plain language
Go out of their way to tailor the best d
Have the knowledge and authority to make
Have a positive, can-do approach to doin
Understand your business and the market
Are proactive with ideas on how to get t
Are prompt and reliable in handling any
Treat you with respect and listen to wha
Keep in regular contact to keep you upda
The competitiveness of their fees and ra
Offering a flexible range of lending/rep
How easy it is to take out a commercial
The features and benefits of their comme
Providing a full range of commercial and
Being fair and reasonable in their lendi
Comms
Prod
0.00002
-0.05261
0.12441
0.01660
0.28300
0.23061
-0.00387
-0.09662
0.38097
0.40169
-0.31326
-0.29803
0.06032
0.15380
-0.20335
0.06689
-0.05810
-0.03013
-0.10791
-0.07959
0.04922
0.03159
-0.07805
-0.10390
-0.07577
-0.12283
-0.07319
-0.06241
0.30859
0.28211
0.23604
0.28074
0.21454
0.26368
Expt
0.16224
0.32007
0.09350
0.08251
-0.18644
-0.01169
0.26047
0.32550
-0.14483
-0.21807
0.52827
0.11545
-0.21660
-0.26978
0.06212
-0.16961
-0.06906
Getting to the actual attributes…
 The scoring algorithm tells us how much each
standardised attribute { (x-m)/s } contributes to each factor
score
 So one way to see the importance of each attribute is
looking at the change in modelled score as each attribute
incerases by a value of 1 ( ie 1 s)
 The works out to be
 Importance for attribi = SibjFij
 Easy to compute in Excel (cut and paste output into excel –
hint: use the ‘Text to columns’.., options in the ‘Data’
Alternatively export hold.modelfac to excel via .csv option
Getting to the actual attributes…
Comms Prod
Expt
0.96331
0.5634 0.65804 Importance
Factor1 Factor2 Factor3
Beta's
Factor scores
Q30A13
Q30A14
Q30A8
Q30A7
Q30A3
Q30A11
Q32A3
Q30A2
Q30A6
EXPERT
Q30A12
Q32A2
Q32A5
Q32A6
Q30A15
Q32A4
Q32A1
Are prompt and reliable in handling any
Treat you with respect and listen to wha
Have a positive, can-do approach to doin
Have the knowledge and authority to make
Communicate clearly, in plain language
Understand your business and the market
How easy it is to take out a commercial
Take the time to understand who you are
Go out of their way to tailor the best d
STAFF - Experts in Commercial Finance Ma
Are proactive with ideas on how to get t
Offering a flexible range of lending/rep
Providing a full range of commercial and
Being fair and reasonable in their lendi
Keep in regular contact to keep you upda
The features and benefits of their comme
The competitiveness of their fees and ra
0.38097
0.40169
0.23061
0.283
0.12441
-0.00387
0.1538
-0.05261
0.0166
0.00002
-0.09662
0.06032
0.06689
-0.0581
-0.31326
-0.20335
-0.29803
-0.12283
-0.07319
-0.07805
0.03159
-0.07959
-0.1039
0.23604
-0.10791
0.04922
-0.03013
-0.07577
0.28211
0.21454
0.26368
-0.06241
0.28074
0.30859
-0.14483
-0.21807
-0.01169
-0.18644
0.0935
0.26047
-0.26978
0.32007
0.08251
0.16224
0.3255
-0.2166
-0.16961
-0.06906
0.52827
0.06212
0.11545
0.202486
0.202218
0.170483
0.16773
0.136531
0.109134
0.103616
0.099143
0.098016
0.089804
0.078428
0.074516
0.073697
0.047145
0.010695
0.003157
-0.03726
NB: compute importance using this type of code:
=SUMPRODUCT(C6:E6,C$3:E$3) where C6:E6 is the
attribute say and C$3:E$3 are the beta’s.
Conclusions
 Note how things have changed: